The purpose of this study was to examine the effect of using Lakatos’ heuristic method to teach the surface area of the cone (SAC) on students’ learning. The Lakatos (1976) heuristic framework and the Oh (2010) model of “the enhanced-conflict map” were employed as framework for the study. The first research question examined the impact of the Lakatosian heuristic method on students’ learning of the SAC, which was addressed in three sub-questions: the impact of the method on the students’ achievement, the impact of the method on their conceptual learning and the impact of the method on their higher order thinking skills. The second question examined whether the heuristic method of teaching the SAC helped students to sustain their learning better than the traditional method (Euclidean method). The third question examined whether the heuristic method of teaching SAC could change students’ readiness level, according to Bloom’s taxonomy. A pre-test and post-test quasi-experimental research design was used in the study that involved a total of 198 Grade 11 students (98 in the experimental group and 100 in the control group) from two schools in Cyprus. The instruments used for data collection were cognitive tests, lesson observations (video-recorded), interviews and questionnaire. Data was analysed using inferential statistics and the Oh (2010) model of the enhanced conflict map. Student achievement within time was the dependent variable and the method of training the independent variable. Therefore, time was the “within” factor and each group was measured three times (pre-test, post-test and delayed). The differences in students’ achievement within each group over time were examined. Results indicated that the average mean score achievement of the students in the experimental group was double that of the students in the control group. The Jun- Young Oh’s model of the enhanced conflict map showed that students in both groups changed from alternative conceptions to scientific conceptions with the experimental group showing greater improvement. It was also observed that from the post-test to delayed test, the Lakatosian method of teaching the SAC has a significant positive effect on students’ achievement at all levels of Bloom’s taxonomy, especially at the higher order thinking (HOT) levels (application and analysis-synthesis levels) as compared to the Euclidean method of teaching. In addition, the Lakatosian method helped the students to sustain their learning over time better than the Euclidean method did and also helped them to change their readiness level, especially at the HOT levels. The Lakatosian method helped students to foster skills that promote active learning. Of great importance was the use of mathematical language, as well as, the enhanced perception in the experimental group in comparison with the control group, through the use of the Lakatosian method. The results of this study are promising. It is recommended that pre-service teachers should be trained on how to effectively implement the Lakatosian heuristic method in their teaching. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education (Mathematics Education))

The purpose of this study was to examine the effect of using Lakatos’ heuristic method to teach the surface area of the cone (SAC) on students’ learning. The Lakatos (1976) heuristic framework and the Oh (2010) model of “the enhanced-conflict map” were employed as framework for the study. The first research question examined the impact of the Lakatosian heuristic method on students’ learning of the SAC, which was addressed in three sub-questions: the impact of the method on the students’ achievement, the impact of the method on their conceptual learning and the impact of the method on their higher order thinking skills. The second question examined whether the heuristic method of teaching the SAC helped students to sustain their learning better than the traditional method (Euclidean method). The third question examined whether the heuristic method of teaching SAC could change students’ readiness level, according to Bloom’s taxonomy. A pre-test and post-test quasi-experimental research design was used in the study that involved a total of 198 Grade 11 students (98 in the experimental group and 100 in the control group) from two schools in Cyprus. The instruments used for data collection were cognitive tests, lesson observations (video-recorded), interviews and questionnaire. Data was analysed using inferential statistics and the Oh (2010) model of the enhanced conflict map. Student achievement within time was the dependent variable and the method of training the independent variable. Therefore, time was the “within” factor and each group was measured three times (pre-test, post-test and delayed). The differences in students’ achievement within each group over time were examined. Results indicated that the average mean score achievement of the students in the experimental group was double that of the students in the control group. The Jun- Young Oh’s model of the enhanced conflict map showed that students in both groups changed from alternative conceptions to scientific conceptions with the experimental group showing greater improvement. It was also observed that from the post-test to delayed test, the Lakatosian method of teaching the SAC has a significant positive effect on students’ achievement at all levels of Bloom’s taxonomy, especially at the higher order thinking (HOT) levels (application and analysis-synthesis levels) as compared to the Euclidean method of teaching. In addition, the Lakatosian method helped the students to sustain their learning over time better than the Euclidean method did and also helped them to change their readiness level, especially at the HOT levels. The Lakatosian method helped students to foster skills that promote active learning. Of great importance was the use of mathematical language, as well as, the enhanced perception in the experimental group in comparison with the control group, through the use of the Lakatosian method. The results of this study are promising. It is recommended that pre-service teachers should be trained on how to effectively implement the Lakatosian heuristic method in their teaching. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education (Mathematics Education))